Numerical control apparatuses for turning have been proposed that includes a cutting-tool feeding mechanism that feeds a cutting tool toward a workpiece and a control mechanism that enables the cutting tool to vibrate at low frequency and controls a cutting-tool feed drive motor (see Patent Literatures 1 to 3). The control mechanism in such numerical control apparatuses includes an operation unit that sets various settings; a vibration cutting information storage unit that stores, in advance in the form of a table, at least the advancement amount, retreat amount, advancement speed, and retreat speed of the cutting tool feed mechanism that correspond to the inertia of the feed shaft or machine characteristics such as motor characteristics according to the rotation speed of the workpiece or the feed amount of the cutting tool per rotation of the cutting tool that is set by the operation unit, as data with which the cutting tool can operate at a low frequency of 25 Hz or higher with which the cutting tool is synchronously fed; and a motor control unit that controls the cutting-tool feed drive motor on the basis of the data stored in the vibration cutting information storage unit. Thus, advancement and retreat are repeated along an interpolated path, thereby generating low-frequency vibrations. Additionally, a technique to superimpose vibration in a designated angular direction for contour control has been disclosed (see Patent Literature 4).